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Question: At constant volume and temperature conditions, the rate of diffusion \(\rho _ { B }\) are related by...

At constant volume and temperature conditions, the rate of diffusion ρB\rho _ { B } are related by the expression.

A

DA=[DBρAρB]1/2D _ { A } = \left[ D _ { B } \cdot \frac { \rho _ { A } } { \rho _ { B } } \right] ^ { 1 / 2 }

B

DA=[DBρBρA]1/2D _ { A } = \left[ D _ { B } \cdot \frac { \rho _ { B } } { \rho _ { A } } \right] ^ { 1 / 2 }

C

DA=DB(ρAρB)1/2D _ { A } = D _ { B } \left( \frac { \rho _ { A } } { \rho _ { B } } \right) ^ { 1 / 2 }

D

DA=DB(ρBρA)1/2D _ { A } = D _ { B } \left( \frac { \rho _ { B } } { \rho _ { A } } \right) ^ { 1 / 2 }

Answer

DA=DB(ρBρA)1/2D _ { A } = D _ { B } \left( \frac { \rho _ { B } } { \rho _ { A } } \right) ^ { 1 / 2 }

Explanation

Solution

DADB=ρBρA=[ρBρA]12\frac { D _ { A } } { D _ { B } } = \sqrt { \frac { \rho _ { B } } { \rho _ { A } } } = \left[ \frac { \rho _ { B } } { \rho _ { A } } \right] ^ { \frac { 1 } { 2 } } ; DA=DB(ρBρA)12\therefore D _ { A } = D _ { B } \left( \frac { \rho _ { B } } { \rho _ { A } } \right) ^ { \frac { 1 } { 2 } }